{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from geoist.others import abic\n",
    "from geoist.others import utils\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import pathlib\n",
    "from datetime import datetime\n",
    "from functools import wraps\n",
    "from pathos.multiprocessing import Pool\n",
    "import numpy as np\n",
    "from scipy import linalg as splin\n",
    "from scipy import sparse as spsparse\n",
    "from scipy.optimize import minimize\n",
    "from scipy.optimize import Bounds\n",
    "from scipy.optimize import LinearConstraint\n",
    "import h5py\n",
    "\n",
    "import cupy as cp\n",
    "\n",
    "from geoist import gridder\n",
    "from geoist.pfm import prism\n",
    "from geoist.inversion.mesh import PrismMesh\n",
    "from geoist.others import walsh\n",
    "from geoist.others import toeplitz as tptz\n",
    "from geoist.others import utils\n",
    "from geoist.others import abic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Structure of smooth constraint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose unkowns are arrange in the order: first along x-axis, then along y-axis, then along z-axis. The vector of unkowns will have shape (nz,ny,nx). \n",
    "Under such assumption, we get smooth constraints as follows.\n",
    "### Along x-axis\n",
    "The constraint alone x-axis is built by a 3 level hierarchical structure. The smallest structure correspond to one line along x-axis, for example, the 1-st order smooth constraint would be $$ A^{(n_x-1) \\times n_x} = \\begin{bmatrix} 1 & -1 & 0 & \\dots & 0 \\\\ 0 & 1 & -1 & \\dots & \\vdots \\\\ \\vdots & \\vdots & \\vdots & \\vdots & \\vdots \\\\ 0 & \\dots & 0 & 1 & -1 \\end{bmatrix}$$\n",
    "The 2-nd level correspond to one layer and is built by $A$ in the form of $$ B^{n_y \\times n_y} = \\begin{bmatrix} A & 0 & \\dots & 0 \\\\ 0&A &\\dots & \\vdots \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots & A\\end{bmatrix}$$\n",
    "The 3-rd level correspond to the whole grid and is built by $B$ in the form of $$ C^{n_z \\times n_z} = \\begin{bmatrix} B & 0 & \\dots & 0 \\\\ 0&B &\\dots & \\vdots \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots &B\\end{bmatrix}$$\n",
    "\n",
    "Using these formulas, we get $$C^TC = \\begin{bmatrix} B^TB & 0 & \\dots & 0 \\\\ 0&B^TB &\\dots & \\vdots \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots &B^TB\\end{bmatrix}$$\n",
    "\n",
    "$$B^TB = \\begin{bmatrix} A^TA & 0 & \\dots & 0 \\\\ 0&A^TA &\\dots & \\vdots \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots &A^TA\\end{bmatrix}$$\n",
    "\n",
    "$$A^TA = \\begin{bmatrix}1& -1& 0 & \\dots & 0 \\\\ -1 & 2 & -1 & 0 & \\vdots \\\\ 0 & \\ddots & \\ddots & \\ddots & \\vdots \\\\ \\vdots & \\ddots & -1 & 2 & -1 \\\\ 0 & 0 & \\dots & -1 & 1\\end{bmatrix}$$\n",
    "\n",
    "### Along y-axis\n",
    "The constraint alone y-axis is built by a 2 level hierarchical structure. The smallest structure correspond to one layer, for example, the 1-st order smooth constraint would be $$ A^{(n_y-1)n_x \\,\\times \\,n_xn_y} = \\begin{bmatrix} 1 & 0 & \\dots & -1 & 0 & \\dots & 0 \\\\ 0 & 1 & 0 & \\ddots  & -1 & \\ddots & \\vdots \\\\ \\vdots & \\ddots & \\ddots & \\ddots & \\ddots & \\ddots & \\vdots \\\\ 0 & 0& \\dots &1  & 0 & \\dots & -1 \\end{bmatrix}$$\n",
    "There are $n_x -1$ zeros between $1$ and $-1$ in each line.\n",
    "\n",
    "The 2-nd level correspond to one layer and is built by $A$ in the form of $$ B^{n_z \\times n_z} = \\begin{bmatrix} A & 0 & \\dots & 0 \\\\ 0&A &\\dots & \\vdots \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots & A\\end{bmatrix}$$\n",
    "\n",
    "Using these formulas, we get $$B^TB = \\begin{bmatrix} A^TA & 0 & \\dots & 0 \\\\ 0&A^TA &\\dots & \\vdots \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 0 & 0 & \\dots &A^TA\\end{bmatrix}$$\n",
    "\n",
    "$$A^TA = \\begin{bmatrix}1& 0 &\\dots & -1& 0 & \\dots & \\dots & \\dots&\\dots & 0 \\\\ 0 & \\ddots & \\ddots & \\ddots &\\ddots  &\\ddots &\\ddots&\\ddots&\\ddots&\\vdots \\\\ \\vdots & \\ddots & 1 & \\ddots & \\ddots  &\\ddots&\\ddots&\\ddots&\\ddots  & \\vdots \\\\ -1 & \\ddots & \\ddots & 2 & \\ddots & \\ddots &\\ddots&\\ddots&\\ddots& \\vdots \\\\ 0 & \\ddots & \\ddots & \\ddots & \\ddots & \\ddots &\\ddots&\\ddots&\\ddots&\\vdots \\\\ \\vdots & \\ddots & \\ddots & \\ddots & \\ddots & 2 &\\ddots&\\ddots&\\ddots&\\vdots \\\\ \\vdots & \\ddots & \\ddots & \\ddots & \\ddots & \\ddots &1&\\ddots&\\ddots&-1 \\\\ \\vdots & \\ddots & \\ddots & \\ddots & \\ddots & \\ddots &\\ddots&\\ddots&\\ddots&0\\\\ \\vdots & \\ddots & \\ddots & \\ddots & \\ddots & \\ddots &\\ddots&\\ddots&\\ddots&\\vdots\\\\ 0 & \\dots & \\dots & \\dots & \\dots & \\dots &-1&0&\\dots&1\\end{bmatrix}$$\n",
    "There are $n_x -1$ zeros between $1$ and $-1$ in the first row and first column.\n",
    "\n",
    "### Along z-axis\n",
    "The constraint alone z-axis only have one level, which correspond to the whole grid. The 1-st order smooth constraint would be $$ A^{(n_xn_y-1)n_z \\,\\times \\,n_xn_yn_z} = \\begin{bmatrix} 1 & 0 & \\dots & -1 & 0 & \\dots & 0 \\\\ 0 & 1 & 0 & \\ddots  & -1 & \\ddots & \\vdots \\\\ \\vdots & \\ddots & \\ddots & \\ddots & \\ddots & \\ddots & \\vdots \\\\ 0 & 0& \\dots &1  & 0 & \\dots & -1 \\end{bmatrix}$$\n",
    "There are $n_xn_y -1$ zeros between $1$ and $-1$ in each line.\n",
    "\n",
    "$$A^TA = \\begin{bmatrix}1& 0 &\\dots & -1& 0 & \\dots & \\dots & \\dots&\\dots & 0 \\\\ 0 & \\ddots & \\ddots & \\ddots &\\ddots  &\\ddots &\\ddots&\\ddots&\\ddots&\\vdots \\\\ \\vdots & \\ddots & 1 & \\ddots & \\ddots  &\\ddots&\\ddots&\\ddots&\\ddots  & \\vdots \\\\ -1 & \\ddots & \\ddots & 2 & \\ddots & \\ddots &\\ddots&\\ddots&\\ddots& \\vdots \\\\ 0 & \\ddots & \\ddots & \\ddots & \\ddots & \\ddots &\\ddots&\\ddots&\\ddots&\\vdots \\\\ \\vdots & \\ddots & \\ddots & \\ddots & \\ddots & 2 &\\ddots&\\ddots&\\ddots&\\vdots \\\\ \\vdots & \\ddots & \\ddots & \\ddots & \\ddots & \\ddots &1&\\ddots&\\ddots&-1 \\\\ \\vdots & \\ddots & \\ddots & \\ddots & \\ddots & \\ddots &\\ddots&\\ddots&\\ddots&0\\\\ \\vdots & \\ddots & \\ddots & \\ddots & \\ddots & \\ddots &\\ddots&\\ddots&\\ddots&\\vdots\\\\ 0 & \\dots & \\dots & \\dots & \\dots & \\dots &-1&0&\\dots&1\\end{bmatrix}$$\n",
    "There are $n_xn_y -1$ zeros between $1$ and $-1$ in the first row and first column.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Derivatives in ABIC calculation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Derivatives of sums of determinates\n",
    "Let $A_i$ are $m\\times m$ matrices, $a_i$ are variables, consider function $f(a_1,a_2,...,a_n) = \\log \\det(\\sum_i a_i A_i)$. We want $\\partial f/\\partial a_i$.\n",
    "\n",
    "According to Jacobi's formula:\n",
    "$$\\frac{d \\det(A(t))}{dt} = \\det(A(t))\\mathrm{Tr}\\left(A(t)^{-1}\\frac{dA}{dt}\\right)$$\n",
    "\n",
    "We get:\n",
    "$$\\begin{array}{rl}\\frac{\\partial f}{\\partial a_j} =& \\frac{1}{\\det(\\sum_i a_i A_i)}\\det(\\sum_i a_i A_i) \\mathrm{Tr}\\left((\\sum_i a_i A_i)^{-1}\\frac{d \\sum_i a_i A_i}{d a_j}\\right) \\\\\n",
    "= &\\mathrm{Tr}\\left((\\sum_i a_i A_i)^{-1} A_j\\right) \\end{array}$$\n",
    "\n",
    "If $A_i = B_i^T \\begin{bmatrix}w_0 & 0 & \\cdots & 0 \\\\ 0 & w_1 & \\ddots & \\vdots \\\\ \\vdots & \\ddots & \\ddots & \\vdots \\\\ 0 & \\cdots & 0 & w_{n-1} \\end{bmatrix} B_i$, where $B_i = \\begin{bmatrix} b_0 \\\\ b_1 \\\\ \\vdots \\\\ b_{n-1} \\end{bmatrix}$, then\n",
    "\n",
    "$$\\frac{\\partial f}{\\partial w_j} = \\mathrm{Tr}\\left((\\sum_i a_i A_i)^{-1} b_j^T b_j\\right)$$\n",
    "\n",
    "### Derivatives of min_U\n",
    "In our problem, U is:\n",
    "\n",
    "$$U = \\frac{1}{2}||(a_g G^T obs + \\sum a_i B_i^T constraint_i) - (a_g G^T G + \\sum a_i B_i^TB_i)m||^2$$\n",
    "\n",
    "Solve the least square problem and get it's solution $m_{opt}$, then\n",
    "\n",
    "$$\\min(U) = \\frac{1}{2}||(a_g G^T obs + \\sum a_i B_i^T constraint_i) - (a_g G^T G + \\sum a_i B_i^TB_i)m_{opt}||^2$$\n",
    "\n",
    "Denote $G=B_0$, $obs = constraint_0$ and $B_i constraint_i = r_i$for abbreavity:\n",
    "\n",
    "$$\\min(U) = \\frac{1}{2}||\\sum a_i B_i^T constraint_i - \\sum a_i B_i^TB_i m_{opt}||^2$$\n",
    "\n",
    "After some simple algebra operations, we get\n",
    "\n",
    "$$\\frac{\\partial \\min(U)}{\\partial a_i} = (\\sum a_j r_j)^T + (\\sum a_j B_j^T B_j m_{opt})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "calling forward\n",
      "forward completed in 0:00:00.027920\n",
      "\n",
      "calling walsh_transform\n",
      "generating walsh_matrix\n",
      "walsh transformation of kernel already exists.\n",
      "walsh transformation of depth already exists.\n",
      "walsh transformation of refer already exists.\n",
      "walsh transformation of dy already exists.\n",
      "walsh transformation of dz already exists.\n",
      "walsh transformation of dx already exists.\n",
      "walsh_transform completed in 0:00:00.007909\n"
     ]
    }
   ],
   "source": [
    "print_level = -1 # control indentation of prints.\n",
    "last_print_level = -2\n",
    "mat_count = 0\n",
    "\n",
    "# define model volume and grid shape\n",
    "nzyx = [64,8,128]\n",
    "source_volume = [-47500, 47500, -47500, 47500, 4000, 32000]\n",
    "\n",
    "model_density = np.zeros(tuple(nzyx))\n",
    "for iz in range(40):\n",
    "    model_density[iz,:,75-iz:85-iz] = 1.0\n",
    "\n",
    "refer_density = np.zeros(tuple(nzyx))\n",
    "refer_density[:,:,50:61] = model_density[:,:,50:61]\n",
    "\n",
    "# reference constraint on each cell\n",
    "refer_constraint = np.zeros_like(refer_density)\n",
    "refer_constraint[np.where(refer_density != 0.)] = 1.\n",
    "\n",
    "# depth constraint\n",
    "step = (source_volume[5] - source_volume[4])/nzyx[0]\n",
    "depths = np.linspace(source_volume[4]+step/2.,source_volume[5]-step/2.,nzyx[0])\n",
    "depth0 = 0\n",
    "alpha = 1\n",
    "depth_constraint = depths[0]**alpha/(depths+depth0)**alpha\n",
    "#depth_constraint = np.ones(nzyx[0])\n",
    "\n",
    "weights = {'dx':23.54,'dy':860.,'dz':60.28,'depth':1.,'obs':1.69,'refer':0.67,'bound':1.0}\n",
    "\n",
    "small_model = abic.GravInvAbicModel(nzyx=nzyx,\n",
    "                       source_volume=source_volume,\n",
    "                       model_density=model_density,\n",
    "                       refer_density=refer_density,\n",
    "                       depth_constraint=depth_constraint,\n",
    "                       weights=weights,\n",
    "                       smooth_on='m'\n",
    "                       )\n",
    "small_model.gpu_id = 2\n",
    "#small_model.constraints['refer'] = refer_constraint.ravel()\n",
    "small_model.gen_mesh()\n",
    "small_model.gen_kernel()\n",
    "small_model.forward()\n",
    "small_model.min_density = 0.\n",
    "small_model.max_density = 1.\n",
    "orig_obs = small_model.obs_data.copy()\n",
    "#small_model.obs_data += np.random.randn(*small_model.obs_data.shape)*np.max(np.abs(small_model.obs_data))*0.01\n",
    "small_model.walsh_transform()\n",
    "#small_model.do_linear_solve()\n",
    "#small_model.abic_optimize()\n",
    "#small_model.lasso_optimize()\n",
    "#small_model.calc_abic()\n",
    "#%time small_model.bound_optimize()\n",
    "#recovered = (small_model.kernel_op.gtoep.matvec(small_model.solution.ravel()).reshape(nzyx[1],nzyx[2]))\n",
    "#res = (recovered - small_model.obs_data.reshape(nzyx[1],nzyx[2]))\n",
    "#print(np.linalg.norm(res)**2)\n",
    "#print(np.linalg.norm(small_model.solution.ravel()-refer_density.ravel())**2)\n",
    "#small_model.calc_res()\n",
    "#small_model.print_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "small_model.abic_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['dx', 'dy', 'dz', 'depth', 'obs', 'refer', 'bound']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(small_model._weights.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "calling do_linear_solve\n",
      "do_linear_solve completed in 0:00:20.383453\n"
     ]
    }
   ],
   "source": [
    "small_model.do_linear_solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "calling calc_abic\n",
      "    calling calc_log_prior_total_det\n",
      "    calc_log_prior_total_det completed in 0:07:26.164076\n",
      "\n",
      "    calling calc_u\n",
      "    calc_u completed in 0:00:20.746675\n",
      "\n",
      "    calling calc_log_obs_det\n",
      "    calc_log_obs_det completed in 0:00:00.000040\n",
      "calc_abic completed in 0:07:46.911742\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "28.70300664828801"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "small_model.calc_abic()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 1296x1296 with 2 Axes>,\n",
       " <mpl_toolkits.axes_grid1.axes_grid.ImageGrid at 0x7fc7f6366668>)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "utils.plot_matrix(small_model.model_density.reshape(nzyx)[:,5,:],fname='orig.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 1296x1296 with 2 Axes>,\n",
       " <mpl_toolkits.axes_grid1.axes_grid.ImageGrid at 0x7fec15b206d8>)"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AAAAA1ozo0vms6z8bAgAAAACABx4rKwAAAAAAmEn0q+e4HFoRAAAAAACsCisrAAAAAACYA9+smA0vKwAAAAAAmEXiZcVMrvRlRUpJm+3L7zKKuHNcUo+LQXrxmGrKWo7XxgMFx5vHujieMD4slc/HxjcGzdC5OK7qKCkfDduZJjSnGWoZdFwgomv7MYjNcuc6NZxrGN9WsNTAnBuir6auPhJuqQjXQ0Tv2nqD6+3Gu37jxg5f72ZTbuCNqddFiJ5ta6JLzbZuO0k62pbLj010qUnOlOTjSY+3Ln7Ujw9HJoLUlR13Pqbu2EWXJh9dujHxpCmb84nuqaNyI24fvlUsu/nYQ7be/qg8TXL31M3HfMTo8eseK9f7yKuLZbsb5VhTSTqZbhTLTofy8UaRh6OZe9j40Ya4STtXaogmdPOAaOx2Y6UblaZUH3d/CO5WlHw05LCvz8G113yhOU1nnkMtUxrXCtHPJq4N22I5l4k3t7e5OddoeHDxr66vRD+jRXMerAsrKwAAAAAAmAkrK+bBBzYBAAAAAMCqsLICAAAAAIAZpER06VxoRQAAAAAAsCqsrAAAAAAAYCbRR8ZxOaysAAAAAAAAq8LKCgAAAAAA5pASaSAzudKXFX3f6aFX3XzZsihrdxrKmcO+zNfr8pV7s3wn6oC9WbSyVO54y3YuvzotlP/tPzzjM6i7IAO8xGU2S9JkjqncU5YTZUWPpp1q2yjis7j98VaP2w2N77p+1B8cd67Rebo2dNc8ygbvN3XburFOkjam3s4c73br+8NmU96v2+d2Gx1vufzIbHu0tdVqa56Yx2bb7caPocfbcj883pTLjvrys0+Stn15221X3vao8w/OTSqXuzJJ6iZ/zEW9vzjp5q1i2dEjD5c3DMaAo4dPi2Vu/nD02CO23u3rX1csGx95TbHs5PhVtt5743F52135ntrt/HUZx3I75YY5Qst8yJlMvdld8uBZU/sM68x4tkbRZRnMvLszE8ouqNj9UOL6YMuHDN01jeb6rv/WlrWI5giuvAu2ddxcaufGjoZ2cNfm+Lg8DkoNc1EcBCsrAAAAAACYCWkg8+BlBQAAAAAAMziLLmUJxxx45QMAAAAAAFaFlRUAAAAAAMyElRXzYGUFAAAAAABYFVZWAAAAAAAwi8QHNmdytS8rUjnmLo7HLOdJtcQPOi2ROm5TG1sYLHaZunLFLnaoZSnSUhFLLWrPpyVa07VDS/u6baO2d+eTFhojW1a1uZjLpQRXvL5e0xDRebptXWRn1M/cti6eNIrIXVvE6CZ4ch1VRoxuen+/HW3L5Udm262JH5V8jGht/Kgk9cnUa7Z120nSNu2LZV2ujCaVlDvznN8e2W272w8Vy/pHy/GjxyZ+VJK2+3IUa3dUPqb+VT5iVK/9nmLR6cOvL5a90D9qq33+pBzZd7fcDDo58ddtvyu3w7A38fEmtjAyji6WPoghN/t1EZhRjLN7ANpY74ZYSKflZyE3dW6Zk7eYKts3nivVtX9Ub+30ODoe97NAS1SwY6Nh8/p+hmiJWsX1wsoKAAAAAADmQBrIbFifAgAAAAAAVoWVFQAAAAAAzIJvVsyFVgQAAAAAAKvCygoAAAAAAObCR0BnwcsKAAAAAABmkPjA5myu9GVFnrJ2J+XIs1o2LqohqnIpLsZnWiiS6FDtcIjU00P8jthSsVmRQ/Tflng2F9nptj3UgO/jSeujQHsXXbotb+tiQs/2Wxcx6iJEo3IbMRqk221NjKiPH/X323bjYkRd/KiPQ+xNdPS2r4sJlaRNMlGKXblsE0SMugjSzuxzo3JM5dl+TZznVB9dOnXlDjEe37bbplu78jG57W7esvX22cT5bcsxofnhR2y9+0fL0aUv3C5Hl357eNjW+/xJ+cZ54U65/96966/5qZm77U/LZYOJfo24Z8Iw+H7mYhh9rGkwVzJjWkuYZ+20pSUStTcH3DIVzdnEbtYn2VpTWmiyGVyXzsz9spvvBFGgtXGfU7Cd7WcN18b/HFYfOeu4e9yVYR4ppXdL+ojOhr6P5Zw//JLyn5P0b57/8Zak1+ecHz0vGyX91nnZ7+ec3+P2Fb6sSCl9XNIPS/p6zvlPnP/dY5J+SdL3SvpdST+Sc/7WZU4OAAAAAID71f36gc2UUi/po5LeJemrkj6XUnoq5/yFF/+dnPN/fuHf/48lvf1CFfdyzj9w2f1dphX/Z0nvfsnf/bikz+Sc3ybpM+d/BgAAAAAA96d3SPpSzvnLOeedpE9Keq/59/+ypF+s3Vm4siLn/PdTSt/7kr9+r6QfOv//n5D0WUk/VnsQAAAAAABceyld529WvDal9PSFPz+Zc37ywp8fl/SVC3/+qqQ//XIVpZTeIumtkn79wl/fOK9/kPThnPPfcQdT+82KN+Scv3b+//9A0htK/2JK6YOSPihJtx95vHJ3AAAAAABgQd/IOT8xU13vk/SpnPPFDw29Jef8TErpj0j69ZTSb+Wcf6dUQfMHNnPOOaXyl23O38Q8KUmv/Zf+1AE+twgAAAAAwNW4X79ZIekZSW++8Oc3nf/dy3mfpL928S9yzs+c/++XU0qf1dn3LIovK2pb8Z+nlN4oSef/+/XKegAAAAAAwPp9TtLbUkpvTSkd6eyFxFMv/ZdSSn9U0qsl/Z8X/u7VKaXj8///Wkk/KOkLL932otqVFU9Jer+kD5//769W1gMAAAAAwH3jGn+zwso5DymlD0n6NZ1Fl3485/zbKaWflvR0zvnFFxfvk/TJnL8rDPmPSfr5lNKks0UTH76YIvJyLhNd+os6+5jma1NKX5X0Uzp7SfHLKaUPSPo9ST9yuZOThn1dBrvN8DV5xS4DWZK0KQdNL9XH3Ll0C+UcH4o7pIZ4ZStP5UaMlmS5YzpE8x7qmrrs9s7di0Hmu+37TfXa4vI+g3q7vlyxuzSbrT+gzaZc7sv88bpyV3a09fUebctlW/MUOQqeMNtN+YY73pbLtr0fKF25Lev888mV92bw3iRfb2/Ku1Sut5dvh07les1vbyrJD86u3sjUlZ+5Y39U3ufRTV/x7fIx99tyvenWztdrBpfx6LhYtr/1qK32zu3XF8ue1WPlstNbtt5v3ykf75275et2cm9v692fDsWyYW/Kdr5e90x24/5mW+5HZ8dk7lU3rpsySepH8wwzfSX19c/y2udxCzONkiS5R2dvjimH7VD3MHfjmSR9989Klxe1gzvclE3h2DDZN5bqD5FsJs+2LLgu00I/KNT2B3xHzvnTkj79kr/7yZf8+b9/me3+gaTvfyX7ukwayF8uFP25V7IjAAAAAADuZymt8z8iX0fNH9gEAAAAAACSlKT79wObV4pWBAAAAAAAq8LKCgAAAAAAZhJ9bw2Xw8oKAAAAAACwKqysAAAAAABgDilOIMTlXOnLipyzxsq4ns7Ek6bJxCS1fIm1IdbURnbazrtMnBEePC3Lz2pjRHsTuxluayLNWr6o7GLUonrdMbn4uzhitG7bbRgx6qJLzXZhxGi5zEWMujLJx4gebcplx31LxGi5LIoudRGjtqwhYtRFl0YRo1F5eTt/vKkh9m1K5efqsLnRUG+5k44m9rSb/DWf+nK9w7YcI3rv6FW23m93Lp70oWLZt+6YHGFJz98pl925U44R3Z0E0aUmgtRFl07BnM/1pcmMzy6aVJJ6U+5iT6PjHUcXe1reLr5namO9g2orRRGYLvoxu/l6UK9rJ/dzQDhzrpxaRz9rjmPdWBjFptufXQ7wY4KLHw23Ndc0+pmwdr85zJzFdcLKCgAAAAAAZpGILp0J61MAAAAAAMCqsLICAAAAAIA5JMW/R4RLoRUBAAAAAMCqsLICAAAAAICZ8M2KefCyAgAAAACAGSQlpcQvMMzhyl9WRLFQJTYKycUhBr/pMnXlWJxkom98/Gi9KJPXxfGsMc+3Ie0Il1AbTxrFktXGk0bHUxtP6uJHo21r41Kj8tr40ajcxY/G0aXlMhc/GkWXugjSo62JGDXxo5J0ZCJIj/pyHGIUMerKN6lc78bEj0pSr/K2LmK0i6JLc3m/LTGhTjZRiS1cNKkkZTN5c9uOne+kvYk9Tbk+xm7oj4plp305uvTOdNvW++3Tcvk37x6Xt7vjr9tzz5f70t275fjR0yC6dDRRoNNYLosiBN2lmXrTH8w+z46pXLGLS4yiFDtT3o8mfjT6ocU8ayYzkYqf5X63Vy2aI7hIT/NjQPhpAHdVW2I53fl0ycS7hhGudReu5VxauHhS13+j43Xjx+Tic/nh477CygoAAAAAAOaQJPFrILNY33+KBwAAAAAADzRWVgAAAAAAMJM1/nr+dUQrAgAAAACAVWFlBQAAAAAAMyG6dB6srAAAAAAAAKvCygoAAAAAAOaQkhRFFuNSrvZlRc5h5naZueCmyGX/Sj6LN5uMZJ/avNxHVZaq10USu1VMLVHG9X1huX269q1toxZRJrnj8tejet3SNbdtb7LiW+qNltK5/fZ9+Zp2wfFuNuXyrSlz20nSxux3uy2XHW1ttTo25Vsz2h9v/X1xvCl3/qPNWFUmScdduXzbD+WyVC6TpE1XLt+oXNYnf7y92bbL5TZMpkySksrt67bNwUQoy/RDs63dTlI292puWLA5pHIHdm0kSerr9jkFx7vPR8Wyk/G4WPbC/oat99v3yts++0L5ZJ57wbfDnTv7YtnJ3XLZ7qRcJknDvtz33TxqCuZgzjSW78c8+enraLadhvI9NY7+eDeV5xrNldx+e9O3o2mUmwc4U8vkroGdI5j2zX7ofmBEcyV3r9rtgvvY9ZdoW1uvu+Zunwfqv1gGKysAAAAAAJgJ36yYBy8rAAAAAACYC9Gls6AVAQAAAADAqrCyAgAAAACAGaSUmr47h+9gZQUAAAAAAFgVVlYAAAAAADAXvlkxiyt9WZFVjqHpgqUyPnLSxE3a+FEpufLKKLT7jUsAOkT86HXkYpRavhZcG08a7dPW2zD2umNyhxRGrbp6XaxpFIlqyl0buWhSKYpENdsFY5IrPzLxo1tTdlZevs9dPKmLJpXq40mPOh+z6CJGXTxpn30kamfy8VxZFLtZHU8aRKLmVPcQc9GkkjSZh2MUBZpzuW5XbxSnOpnyMZfrdWWSdDqW41TvDeWyO6c+Z/jZOyae9E55uxde8PfUXRNPenJvVyxz0aSSNA4uRtT034Y5go0mbIilH8fyMU3mPCVp3JT7dz+6uahvh87c55N7vnVRpKQtLoqjKuvqvd+0xHJiufEh3Jbrdq2wsgIAAAAAgJkQXToP1qcAAAAAAIBVYWUFAAAAAABzSKnt96bxL9CKAAAAAABgVVhZAQAAAADAXPhmxSx4WQEAAAAAwEwSvwYyiyt9WZEUR5SuSSlmVZL6IEZtKdctKrQlWshZ2xd2o9Nc2eHa2E0pihhtiER18aQ2JtRWq95Ehbp9uu2i8toySerN+bhzjaNLyx3RlgXxd5uuPO5sTCRfH0SXblyMqCsz0aThtiae1MWPRuUuntRFk7awsabRtuYZ5iJEz8rL+x2zn1YMJirU1+uPaZjqtt2N/nhPhvK2d3flbV+456+NjSe9U+5nd+742N57d8rxpPvTct+PokunsXxMoymL5gBu3G+JRHX7nUx0qYs1DbcdymVh/LYdg007mCjgs/2Wy9yzJppquujHpkjJheaMtaaG41nZqUiK7rdlDniN/SG6H7EurKwAAAAAAGAOZ/+F/tBHcV9gfQoAAAAAAFgVVlYAAAAAADCLpBT9DjMuhVYEAAAAAACrwsoKAAAAAADmwoc8Z8HKCgAAAAAAsCqsrAAAAAAAYA5JPh8Yl3a1LyvSMh8bcbnBXRAbY7d9gJbvHCLbejI53VHb1x6vu95n9Qbh4sV66/u1O5fU1/fB6Fz9tnX1xlnyddu2ZGL7eqNt5y+TpL43ZabtXVl8TOV+1nf+furMtq7eJF+vK+9T+V50+4zqrS0Lt811Y4ckZXPDZZUvqiuTpCmVO9qYyo//KVh0OebytkM2nVvSYLbdT+Vth8lPV9y2p2O5bDf4cz3Zl8vvnLgyW62ev1PuL3fujMWye3f3tt7Tk3L5flcuG/eDrXcaysfknmHxM9UNeOWi0RyPJI1juXxj+ko0txgb3YQkAAAgAElEQVRHMy6ZY4qex+6Z69rI3212U5kmCrl2ck2YzbxvSbaPNhxT7Vz0EHPuQ+63Vu089rqdJzxWVgAAAAAAMIvENytmwssKAAAAAABmQnTpPGhFAAAAAACwKqysAAAAAABgDknRx2hwSbQiAAAAAABYFVZWAAAAAAAwiyQ1pPLhO678ZUVLnGKxzoW+tmqjNcOUuvoYu1prix89VL0u9jRqoyX6p+SjvA4xli11z7Sci/sOUUsEsVuFF337yJXXxo+G9brY2CgS1USQLvVRaneqcTRsZQRxGDF6gPG3YbmniyB18aOuTKqPJ3XRpJKPJ3XRpFIUMbotlu1M/GhUfmriSU92QXTprnxt7p6Wt7tz1/fRe/fKuZF3TTzpyd2drXd/Wo4g3Z+W6x2C6FIXBeriScNYSLOtnYMF9bpnvYsfdWWS1Jny3gzeU1DvZJ9xblvff90Qe91+jnLp0NNC89+o/9qY1jC2d373W2Tn/XY+qMPKCgAAAAAAZpAkJb5ZMQtaEQAAAAAArAorKwAAAAAAmEPS9ftdq5ViZQUAAAAAAFgVVlYAAAAAADCL5L/wjkvjZQUAAAAAAHNZKobtAcMrHwAAAAAAsCpXvrIiVb5lCrO6r5FD5Aa7vPJDce2QGj5KY7PZg/5Xe0xRnnbqrtd7waidarn735f5el13cecSjUeu3NYbXG53vO6QulR/H7tDSvL1pob9LiEruI/N2WZzrlG9U+r9gVVy9U6mM03yxzOZdhhz+fE/ZF/vaMr3k992N5X3uxvL254Mfrpysi+f68muXHa6t9Xq3okpOy33pbv3Rl+vKT89GYplu125TJL2u/IJjfvyttPgj9eVT6Pf1jLPRrfP3Pt+5uaM7jkfzTXdtuNYngdEcxr//Cuf6yg/9+h7N34s85yvbXtpubmqO6ZpoTm5O9dDzcnX9rNUSzsc4mepV+yazf3XilYEAAAAAACrwjcrAAAAAACYQ+IDm3OhFQEAAAAAwKqwsgIAAAAAgLk0fH8P38HKCgAAAAAAsCqsrAAAAAAAYC58s2IW4cuKlNKbJf0tSW+QlCU9mXP+SErpMUm/JOl7Jf2upB/JOX/L1yV1hSUxUXRQbeRpZKn4zLVFFl2LiJ8LouOtvTZR2y8V2emiTScTbZTCvuLiVE18WBfFh5XLerPPqJv586lv+9rY0+hym9S3IGLU11vbzaLtFuq+i8nZXZzK7SRl0xAuJtRtJ/n+6+Jfw6hVd7wmntRFiEbbunjSqN69iT110aSStBsro0tNNKnk40lPdma7U1utjSe9d688rp8E0aW703KM6N7Ek457X68rH0x0qSuTfDzpaCJGo9juzkVvmnjSKC7cHdNmW+6DYYSreShkVxY8HF2kpItE7YMF0i7a1Mdv18e8t8VRmrIVzp2jfrg2bq7UEu96iGvT8jMarpfLvPIZJP2XOec/LunPSPprKaU/LunHJX0m5/w2SZ85/zMAAAAAAA+ulK7nPysTrqzIOX9N0tfO///zKaUvSnpc0nsl/dD5v/YJSZ+V9GOLHCUAAAAAAGt39usEhz6K+8IrasWU0vdKeruk/0vSG85fZEjSH+js10QAAAAAAACaXPoDmymlhyT9r5L+s5zzcxd/7ynnnFNKL/sLSymlD0r6oCTdetXjbUcLAAAAAMCarfBXKq6jS62sSCltdfai4n/JOf/t87/+5ymlN56Xv1HS119u25zzkznnJ3LOT9y49dgcxwwAAAAAAO5jl0kDSZJ+QdIXc87/44WipyS9X9KHz//3Vxc5QgAAAAAArguiS2dxmV8D+UFJPyrpt1JK//j87/4bnb2k+OWU0gck/Z6kH4kqyjmOv1kTG1nU+6U9S8WT1kaQXrfo0sghIouWakM3lkX7nF7+t68kSX3QRx0bH2b2mRr26Sx1vVu+fdQSieq4U43q9ds2xMmZqFAX3NaQvKvJFHZBFOhkFg26iNFosaFrw5boUne8UzZlJppUqo8nddtJ0t7Gj0bRpS6etFy22/s2PN2Xy1w8qYsmlaSTk3IPPz0tx1y6Mkna7crlexdr6k5U9fGkLppU8lGgNrYwiHZ0fb9zkd/B4OIiJd25dC6vWlJnYkRdWfQMW+wZZ8Zumxy9UPxouO0BIjDXqHa+2RI5u0bufK7buaDeZdJA/g+Vp5R/bt7DAQAAAADgmiINZDa0IgAAAAAAWJVLp4EAAAAAAIAAaSCzYGUFAAAAAABYFVZWAAAAAAAwF9JAZsHLCgAAAAAAZpH4NZCZ8MoHAAAAAACsypWvrFgiQzk1vLlyx5OKia1xxrfdZ0M2sNv2QcqnXiqD+hBcHryCzHd3zV3ZFLRf36+vnWotlRzlbrcH6FZUzm6c9I0/mfflbtsp9cExlbdNKt9vSf7CpVR3YeN2KJ/P6Noh+O8NYy7XO0zlbd12krSfyuX70R/Tyb5cfrov96Xd4Mek/VAuO92Vr9tuZ8ZfSaem/PR0LB/PrlwmSbuTvdm2fDLD3tc77Mr1TkN529GUtYjmJe6q2uebe25G29p6/fG68mksH9MYzD2SfVD5c/VcveVz6cy4LtXPu1vmqW7e0jSvdnOloNqW/dZaap/RvHAJXdCP3M9abj4ftdGV/CyQRHTpTGhFAAAAAACwKnyzAgAAAACAGWRJmW9WzIKVFQAAAAAAYFVYWQEAAAAAwCwS0aUzoRUBAAAAAMCqsLICAAAAAIC5sLJiFlcfXbpANE5aKGax5VhrY3HC2KyGOEqnqzzeln3a2NjgozQuQvAQ8aQtUba9DW9bRtjPOlfeEBVcGb0b3osrjKRdwqEiUW1Mq414jqI1y+WdWfhnUirPtk3lqL/OHG8UXRoVl4wNEaM2wjVo38GUjyZ+1G0nSXsTexpFl+6HuujS03Ii51n5rly227voUn9RXQSpL/O91EWQ+jJfr4vPbLFUNLqLIM1TfTShfda4fQbn6badzH2RBn9dplS+5p2Jap6COOXquOWgvDaR8RDxmBE/36yPwDxErGlkqfvYtqHpK3mZ4eogPwdgOaysAAAAAABgJqSBzIOXFQAAAAAAzCHxgc250IoAAAAAAGBVWFkBAAAAAMBc+DWQWbCyAgAAAAAArAorKwAAAAAAmEttbA6+y7V5WUEMDS6y8UsmCinqRy0RpLVcvJVJQpMkdW5bE1m21PgZxmIdYEmcSZrTWE6Lk+TbyXbBKAGzctuoeV1q4cZFrAVxtK48ZxNdGlzuyW5bbny3Tyk43jCUr05bhGs5mnB0bbRUdGlw4Vw8aRRduhvKdbtUThdNelZevjn2Jrp0v/f9YTDlg4mjdPGjko82dfGkUzRoGS52M+KiCZeKQzyEKWij0Qyy3aYumlvycw+3zxY2sj7YpSs+RGRn2L6VsemHsrbYU9tXVB9Jm4LJaNcwZuH+cW1eVgAAAAAAsG6J6NKZsD4FAAAAAACsCisrAAAAAACYQ5Jkfp0Vl0crAgAAAACAVWFlBQAAAAAAM8msrJgFLysAAAAAAJhFOkgC3v2IVz4AAAAAAGBVVrOyIgUZvovt17z1OtQxHYLLSI7ylWu5tl9KlF1de81bMrEn88owBRnTk8moTjY7/P7q2y4nPefyucbZ7KbMbJqnIJPcbWvKxqDezhzvaCrugnqT6S+duY870/aSNOVy/x1MI/Wp/n7LC/V9V687T0kaTPk49eWyoH19va7t/fHuxnL56d4f034olw1juSwYCjUM5T4xDOWN93tfsdt22JcP2JVJ0jiW651cWfCsyVFDVUrmWeMuTjTGXjfuWe/KpmDMSqaftXDdpe/N/DeYn0Vj+1UL7ws3R2iYvznTAfaJM67tJT9vmdP9/GsgKaV3S/qIpF7Sx3LOH35J+V+V9DckPXP+V/9Tzvlj52Xvl/Tfnf/9z+ScP+H2tZqXFQAAAAAAYJ1SSr2kj0p6l6SvSvpcSumpnPMXXvKv/lLO+UMv2fYxST8l6QlJWdLnz7f9Vml/9+8rHwAAAAAArlpK1/Of2DskfSnn/OWc807SJyW995Kt8m9J+ns552+ev6D4e5Le7TbgZQUAAAAAAIg8LukrF/781fO/e6l/N6X0mymlT6WU3vwKt/0X+DUQAAAAAADmkJJ0fb9Z8dqU0tMX/vxkzvnJV1jH35X0iznn05TSfyjpE5LeWXMwvKwAAAAAAADfyDk/YcqfkfTmC39+k77zIU1JUs75Dy/88WOSfvbCtj/0km0/6w7m2r7yAQAAAABgTbKknNK1/OcSPifpbSmlt6aUjiS9T9JTF/+FlNIbL/zxPZK+eP7/f03SX0gpvTql9GpJf+H874ru+5UVUZyRS+NycX0tXDzmUnFGUXyYi6lqiTWN2v+qRdGkLs4oikKqZaPQorizlb1uXCqONmp6183GsVzYcry5MtZU8udTG2salTdFuJptXZmLzjzb2JSZTbPdUOpc1Krq7+Nk7kfXvlHEqIs2ddtG7eviSfcmfnQwZZK0H8wxjUGcqkn0dLGmexNNKvnoUjcGuJjQs3rL5btdfXTpZBpiclGgUZx15XOq35QjcqP9uiaMxlgbiXrNjKO/5rXcvGWMxkIbtVqut+/9dXHjnRP1h8NEjJbLovvtEBGk91scsOPGh6VimhHLOQ8ppQ/p7CVDL+njOeffTin9tKSnc85PSfpPUkrvkTRI+qakv3q+7TdTSv+Dzl54SNJP55y/6fZ337+sAAAAAADgyqztvyjOKOf8aUmffsnf/eSF//8Tkn6isO3HJX38svviZQUAAAAAADPJC63Qf9Dcv698AAAAAADAtcTKCgAAAAAAZpGU7+NfA7lKtCIAAAAAAFgVVlYAAAAAADAXVlbMgpcVxiEiiSIuCrQlzshtWxtr2lJvC7fPycTQSVIOok1rub7kYsmiGLrkopt6H0XnLBU5G0XHXrXolnFJdC5xryVi1F1Sk0QZ1uviBaMIYpegO5r4OxcFLEmTWdw3ugi7HMQspvLJTkEcsK+4bjMXTSpJg7mwLp7URZNKPp50Z8pcNGlUvjPxo1H5fl9uYBdNKvmx0kWXjsFY5yJIXfzoGESiuuO1cdbB4HKIOL+W+FEXmermCC3PEhvHHvSHUeVrbmPpzZgk+bmH7Q/RHMzU25vxN3rW1M4u4v5r5m8NQ/fKph6LaYmGdfOAqF43BLjxt4UbdzpiTe8rvKwAAAAAAGAOScoL/UfZBw3rUwAAAAAAwKqwsgIAAAAAgBlk0kBmQysCAAAAAIBVYWUFAAAAAABz4ZsVs+BlBQAAAAAAM+HXQOZBKwIAAAAAgFW58pUVtdnYLuPXZQNHbN52w6ucpMrM7CiDujKbPdKSWb42Ldc0mzzoKGf6QTGZPpiC/itzXyzF3TPRLeNOJ2dzjwf1uv26sqjecTLjpIkd74NIclc8mftiMm0UmvpiUU7+gCf3Ht604VJv74fsax5NO41TedvBlEnSbiyX74fyPofRXzdXvh/sptrvXb3li7Pf+84/DOXyYSj3l2Hv+9I4lsvdWBg9yydzTC2SecilzhzvOFbX29kRwnPPVX8u9Xdrnsw1DdqhkxmXzOA9mbaXpGS2dX0wnP+6S1M+lSYtc6XsBmhIamvf2m3D8cz0X7fP6Hq7e7VlfHD1zicpH2DOez9iZQUAAAAAAFgVvlkBAAAAAMBM+GbFPGhFAAAAAACwKqysAAAAAABgDklEl86ElRUAAAAAAGBVWFkBAAAAAMAskjJrAmZx9dGlhSUxLfGj142LAHIRVREXPxrFmtryA9xrcUxSXb0uXkm6v/rhaGNYg3YwkWbZtH0O6rXRbma5XB9ErPnIOHNNTRtJ0mgjk819HNwzrp/Zww36vVtx6OJJo3pdCpiLJ42iNTcuT9Ww0aSSehOH5iJnp6D/Oq5eF00q1bdhFDE6mShbHz/q692ZeNKdiSaV/LhUGz8qSftdOXLSbRs9c93x2nFn8BGYNoY8jIC+PloiRtv2u8yzvPa6hXMwE8eczblEcyHX/K7vh+1nHsqH6L9RFOW0UD+07eTmYEH71vbfqJ/VbhvNnR0333HPTUlKZjLqjjduP14iXCesrAAAAAAAYAZZUuabFbPgZQUAAAAAADMhunQetCIAAAAAAFgVVlYAAAAAADCTLH4NZA6srAAAAAAAAKvCygoAAAAAAGaR+GbFTMKXFSmlG5L+vqTj83//Uznnn0opvVXSJyW9RtLnJf1oznm31IGWIk8lH5PUErfjuOORlosAqo0limKdXLxYSxTSUvFh141rh0O00XWLxmuKnK2NNZU02Zg6E1UZxMm5GFF3qtFlc+UuHjOMRPUpjFXHc6Y87nQmRtSVSdJkoku9Ze7FMfsJi40uNRGjg4kmjbZ18aQumvRsW7dP3/aufDT9zEWIStKwL3diVzYFnX8wJzvsywccRaJO5pkcPa/X5hDxpN2BvrLv5n7umnb9YX5occ9OF2Ee9V93zQ8x7YvnqXX3VFSvm78doo+OwbOvZT5fy/fBhjYyt1RUb+r52eQ6uczoeSrpnTnnPyXpByS9O6X0ZyT9dUk/l3P+PknfkvSB5Q4TAAAAAID1yyldy3/WJnxZkc+8cP7H7fk/WdI7JX3q/O8/IekvLnKEAAAAAADggXKpb1aklHqd/arH90n6qKTfkfRszvnF9ZFflfT4IkcIAAAAAMA1kEUayFwu9Ut0Oecx5/wDkt4k6R2S/uhld5BS+mBK6emU0tOn975ZeZgAAAAAAOBB8YrSQHLOz6aUfkPSvy7p0ZTS5nx1xZskPVPY5klJT0rSY9/zJ6/XV/0AAAAAALisRBrIXMJWTCm9LqX06Pn/vynpXZK+KOk3JP2l83/t/ZJ+damDBAAAAADgOshK1/KftbnMyoo3SvrE+XcrOkm/nHP+31JKX5D0yZTSz0j6R5J+YcHjBAAAAAAAD4jwZUXO+Tclvf1l/v7LOvt+xaWlJHWVAcw51/0GSe3+IrXHsySXzR7loLus6GkoZ8lHuv4V/abRpU1BBnhJS9Z50zWvO9xYX7dZlEFts7gr9xlx7Rs1/TiW/4XeXfMgc3wyXX/s3D5ttRpNvW7MGoPu6y5rb/rgsNCb9Bwcb84mo960b5f8dTtE8lYy+faTOU9JGsyFNV1b+8E38G4o73dv+mA05O/2ZtuhXHZWXj4hdx8Pgx9EXflgTna38yc7mXrtmBWMLa58CrY9hNr5RfSssduasTCa09j2d4+EoO2TGZfccz7qD5OpN1WeixS3fy3XH6bg2tTWa++ZYJLQmWvj+lkLV2/UH5bYZ6R2Xh1p+Tlsqf671DV/KX4NZB60IgAAAAAAWJVl/rM3AAAAAAAPoDV+/+E6YmUFAAAAAABYFVZWAAAAAAAwgyyiS+dCKwIAAAAAgFVhZQUAAAAAADPhmxXzuO9fVrTE3rhYspZ6XaqTSW2SJGUTj9diqRilWmH7mjZ05xLFj7roPCc63r6vi7CK4pX8dXORe8vcF1E3WioR1bW/uzQt8VWjOZlx9PXWjgFRLKTj2mEbbDuZbaeWMdZdG9NXovutdslgCiJRg62LJWNwv02mgV2aXBQxujf9xW3rokklHz/qys6OqVy+37v40fro0v2u3BD7U3+yo7kALbHeh2CjFIP2dWysaZTjXGl0+c+Bzg1o0bamDbtteUrd8qxx7RuNdsnMPVrUzj3a6l1Gyz5r52+LRWdWzmGXZOdnQTtcVcQo1u2+f1kBAAAAAMBVyQ3/MQffwcsKAAAAAABm0rKKGd/BBzYBAAAAAMCqsLICAAAAAIBZJGXWBMyCVgQAAAAAAKvCygoAAAAAAGaQRXTpXFbzsiKKorORW4eIOgoiMA9RbzJ5iD76SprMfvuFosectnZYZnBwfdTFmYX1HiDeKrpnbDypi+oK7mNXbzZdNIrHrO2i4dhRGfsW9V93O7pDGoPIvd5s6w4paga/3/LGm+hB3ZW37ey2/oB31dGEy9xvQxBl6/tDedsoOdOV+7Ig4tkcbxT/7KJNXUyoiyaVpDEor+Wjmutjsv1YaGKnF4pZjLhxv+X55ywVjzmZuVIK2sjNszo7Bwv6g4tcd3OEqJ/ZuV/9jwD+mMplfV+/oNveb0H7Di5ed6E5WGeavi3Ktr4dJjd4N3DX1Z1r1B/8zyZun75eElGvl9W8rAAAAAAA4LpjZcU8+GYFAAAAAABYFVZWAAAAAAAwE1ZWzIOVFQAAAAAAYFVYWQEAAAAAwCwSKytmwssKAAAAAABmkk0yDi6PXwMBAAAAAACrcsUrK5JSevm3TFHmsMvTnbr6zGHLxBFHGeqH4NowN0Qru5xul4G8JJuLXehjrVwfbOkPTX20X+ZcXRv6bGtfrzvX0R2PucclyTV/y5ttd2mSuadstL2k0Zys7b4b3w7jWN7YxY5H3Xc02/Z27PYVd+bauGqn4Jr6/lAuW2jo0GCuS2Q0fWlwN01Qvt+b7Yag3sHcx8F4ZseAsa5M8mOwO6Ro/HVjYWfKgkvjn6vmoo9u8AjqdWWRzj1zzeASPhurj8k/bPx8yOyz7yuPR5pMvX1DvS1zhNGMwakzfSW4bnYeMLm2X2bO6O4ZSZrMfnvTl8LxwfQz1/Zun2vk7n9J6jbLnI/rZ34uWv8z5Vyy+MDmXK7X3QIAAAAAAO57fLMCAAAAAICZsLJiHqysAAAAAAAAq8LKCgAAAAAAZsLKinmwsgIAAAAAAKwKKysAAAAAAJhFakqjw3dc7cuKVI63cRFgER8fVh+TZKNvWqJATSRUFKczVu7YRYtJUmcit9y2brtIS4xa6upjwJYQxaW6vuQit1KwhMxFx/Zm264htslGmpnIMsnHDLvjjeLDJtP+KZW3jeK43H7dMyh6QLk2tLGbUftWRnaGd2LlrbobgrizymF/qYjRqN7a2NMgVc9fG1MW1etSLl0UqIsmbd12GMoH7coio2mMYV/OYnXbSVGMqIkfDZ5vLkrRiZ6btdGQ0RyhNhI1qjcqL2+3zCAQte+wK2f+bo621ft10aY2qr3hGebjXaNnritfJrLTxhO3xLua+zicIwSRyiVL9d9IbTtFP5u4n8O6TblvR81Q20ej443m7FgXVlYAAAAAADCDLGnimxWz4GUFAAAAAAAz4QOb8+ADmwAAAAAAYFVYWQEAAAAAwBxy/P0yXA4rKwAAAAAAwKqwsgIAAAAAgJnwzYp5XOnLiqRyvI2LtonY2KwoQrAh7qhWS2RO9bbhGpplFtnUxpO6SE5JSi6yaFt/LrWxTlH8XWf6oduni90MmVvKxo8G5aOJF+wL0cQviqJYS8LLYqPHysfUEjnrxP3XxC2buMko5c/GnlaWne3YlJmuH9VbO5yFx1u5z+hy1z4uWo7XDS3R8Oq2jWJPHR+vWx976uNHzY0R1HuI57wbd6S26O7aem1kcsPxdDZ2M4ouNc/GoXzNo/jy2kjUpeaiORjsson1ro2OlpaLyIwiPWvVxpNGcxpnqRjLlnpdFKibXyw11i3Wj4KIURdB6p4XUdtHc1WsCysrAAAAAACYReKbFTPh1RIAAAAAAFgVVlYAAAAAADCDLL5ZMRdWVgAAAAAAgFVhZQUAAAAAADPhmxXz4GUFAAAAAAAzWSbz6cHDr4EAAAAAAIBVufKVFbVZvW6zyeRpd0Hm8FCZLR6dR+15TsMy7+GizOGsZfLXXR60E2VF51Q+pmFf3i7KdLb7bMjxdvngLq882mdXmSUfcf3FHdOwH2293WTuVbPPfrPM/TaOvn17W2jaKLhlalcGRl3QlY/m0kTR7K55k+mCDbebPZeG+Hp7TNF1cft1x9swdFRf02hbdx9H94Urb9nW3TfD4E/WPad6c9GjMeu6SeaZkE2Hcdu17DPinvXdxo7AQb3l/mDbKBwMy0XuOZ86X+9kjtc+5xumjO5cwzlu5SAczWlcG7pto+tWO0eI+Lldfb3uePO+/qK7sbBljuv3WT4XN/+VfDv05mZc6nq/UvwayDxYWQEAAAAAAFaFb1YAAAAAADCDrER06UxYWQEAAAAAAFaFlRUAAAAAAMyEb1bMg5UVAAAAAABgVVhZAQAAAADATPhmxTyu9GVFSqkYm9MSk5RM3E6XfPTVOJYjgCZTllbYAV0EUBTPNppIs74vt2F03dzSHRc15aJJz/brosfK2+YDxXHV1ruUKObL3RdOFEPluJjbMTjejdmvT94NoktN5FbLNfWRvsvUO4zuXHy9Lo0yuXjMhlg9d8nNkCQpiLo29UZLDWuT3aLbqTYSNUpZ3O3L/8JuZ/rKEER+N0Rs2/jBhaLzasezFi6KUvLPMDeniWNCzbxluvrn0KEiBH0s5zL1unnLOET1mujS46NiWdS+m215mu+i3F3EpSR1m7pG3J/6hnDzbsfNYSVp05XbwY07wW1s2Qj4aA5WmUm72db/zON+ron6Q+19Hs2jauN1o7noprL/4jBYWQEAAAAAwBxy/B8UcDm8rAAAAAAAYAZZ/BrIXFgHAwAAAAAAVoWVFQAAAAAAzITo0nmwsgIAAAAAAKwKKysAAAAAAJjJQgFXD5wrf1lRipqJ4mtcbI6L4slBNKGLvnExX2FkZ22sYRCn4yKWWuLZXDypi7eK1EbRRfFsrv1dXGIUF+X7yzLt4KKxorgoez5BvKPj4sNcf5iC9k0m59JeN5ePqaAdGtaPjSazs+9NZLKJPJWk7aYuRjS6n0YTTyp3vA0fgbLRmsG2PsLVbBdEMLrhw8WeNgx1TdwY4Lr24DJlJe335YpdPGkUTerK3T0j+Xt1NPWGY7eLlDRl0Rjr9FN522FfXa0VzS18gGM9G7XaEE8aXdf6el0frn84uuefa6MoSrFzEfHmmje1/QFihFu4eNLqObd8+0bXzW7bEI/pzidt6/rgWXldnGq3aZhQLsRdm5ZoeawPKysAAAAAAJhF0kQayCz4ZgUAAAAAAFgVVlYAAAAAADCDLNJA5sLKCgAAAAAAsCqsrAAAAIkd5IMAACAASURBVAAAYCYr/E7ttcTLCgAAAAAAZpL5wOYs+DUQAAAAAACwKpdeWZFS6iU9LemZnPMPp5TeKumTkl4j6fOSfjTnvPOVlLNvo6xzmw1s8uLH0efF1+4zOt7qvOLBp6TXZqhHWdz2eBtyvGXeKk6pfp/TQtnsLkN9qdzxlnpdP3RlLf1harin3Ln2JpM8utyuvDOFUTsMQ/lcXR896uuz2V13MDHzL25dLHG57VPnGzibS+7avuWWcTHpXfDkcvt15xJ9C8uea/1tUd2GUX+YGo6ptt5xXGacjO7VqPyq9b15zksau6FYNpnraucPkibTYVJwnzt2DtYwxtbWu5ToePug/cv1NsxxzTWN2mg0s8ZNNJAabr9LXTf3DIu4Y+q3Zq600D5DZg7h+lI4DJp54WS6aFTvUuPvZlu+35aak88mx3NXXM4rWVnxn0r64oU//3VJP5dz/j5J35L0gTkPDAAAAAAAPJgu9bIipfQmSf+2pI+d/zlJeqekT53/K5+Q9BeXOEAAAAAAAK6DF6NLr+M/l5FSendK6Z+mlL6UUvrxlyn/L1JKX0gp/WZK6TMppbdcKBtTSv/4/J+non1ddg3Y35T0X0t6+PzPr5H0bM75xXWMX5X0eOFkPijpg5L00KNvuuTuAAAAAADAWpx/GuKjkt6ls3cAn0spPZVz/sKFf+0fSXoi53w3pfQfSfpZSf/eedm9nPMPXHZ/4cqKlNIPS/p6zvnzl630opzzkznnJ3LOT9y4/ZqaKgAAAAAAuBZyvp7/XMI7JH0p5/zl8+9VflLSe7/73PNv5Jzvnv/xH0qqXrFwmV8D+UFJ70kp/e75wbxT0kckPZpSenFlxpskPVN7EAAAAAAAYNUel/SVC38u/obFuQ9I+t8v/PlGSunplNI/TCmFn5EIfw0k5/wTkn5CklJKPyTpv8o5//sppV+R9Jd09gLj/ZJ+NaoLAAAAAID72WQSEVfutSmlpy/8+cmc85M1FaWU/gNJT0j6sxf++i0552dSSn9E0q+nlH4r5/w7pTrqc4ukH5P0yZTSz+js91J+4TIbtcVgvjwXLRTFRblYQxcd5OJ0pCAK1EQH7YLoUreti/OMIn5cvS1cvclEl8bqts1Bll82/XNTGVkWcddmqbi+peIFo/bddHVtGEWWuTjVzkSiRtFirtjdb1PQvnlT1/5RjJptftP0UQSmjQI1hVF0phue3T6jOLDORSa7estpkiHfRn5bFzfpIlEHE9sdlY+mIaLxwUYpBifrztXuM4pobIhUruViRFNLxLONhayvN4o9tdtWRh9HEa7ufFy9UzBX8vGO9fNQV6+PpA7mYO54KyPKpXgOXNyuoY3sMzcaH8J47pcXzvVNO9l56oEikX2krxkDgv5g28FsF123lr5fy//st8guHyTfyDk/YcqfkfTmC39+2d+wSCn9eUn/raQ/m3M+ffHvc87PnP/vl1NKn5X0dknzvKzIOX9W0mdf3IHOfmcFAAAAAADo0t9/uI4+J+ltKaW36uwlxfsk/ZWL/0JK6e2Sfl7Su3POX7/w96+WdDfnfJpSeq3OPjfxs25nLSsrAAAAAADAuazLx4BeNznnIaX0IUm/prN1ux/POf92SumnJT2dc35K0t+Q9JCkXzlfBfP7Oef3SPpjkn4+pTTpbEHPh1+SIvL/w8sKAAAAAAAQyjl/WtKnX/J3P3nh///5wnb/QNL3v5J98bICAAAAAIA55Pj7WrgcPkECAAAAAABWhZUVAAAAAADM5D7+wOaVutKXFUmpGDXTm6gjyccEujjUMHVooThKx8X4tESLXTctkVCd+WhNNm0Yxd9F5bXsuS6UuOf22dLLhn05W6w2Jk3y9/gw+EZyEVZTLh9vGPtm6nXxjlE32ptIyd6NZybKTwqOt6GfuTHLxZ42pN/Zc3Ft1CKaWLjylv5Qu8+WiZCL142iS115NIYO+7qOGMVrR/dyyRSMLUvpTKRn6lyGbtAOpsxFHkZjt32eNNzorvU7c7wuZlwKIkZN2Wbrp8V2XDJzjymInHXl26PyMbVcNyeKAnYx5C33lLvPo2u+hNpxJRK1rxtHt8fL/OjWcq7ufGwUc/AQc+Ub83NjFJEdPeOwLqysAAAAAABgJln3ZxrIVeObFQAAAAAAYFVYWQEAAAAAwAyySAOZCysrAAAAAADAqrCyAgAAAACAmZAGMg9eVgAAAAAAMBNeVsyDXwMBAAAAAACrcrUrK5LUm1xcx+X0utzrzdaljjdkAwdfTbEZymO5KMrM7kyOtysb9i633edi1+Z0R1rq7U3GtzPaVHffl1qO123ryqJ+VttHo3OJ9lvS977ejemjzhQcj71tJnNMweG4jG9XNgUZ3u6QvGjDZa5brei/KoxmLOz78sanO1+vuY3lun7UDi673Q75QX+o/a8vUb2juW/cM2owzwPJ9/3wXN2YZe8pf0xO5zpEMCdpOVfHjcGbbXlqFo2Fk7upzH+fip4J7tnYm3E9Ot5k2jeZ53w0V7L7tM9jX6/d1rRRF9Q7TeX+7e7VTVBv7bM8+k+ZtfexayNJ2mzLO3ZjgJ1zB6rbKOD6UtewT3e8Xe8vXB+U17LXvPKekaTOPJM3Zux2zz5Jymn5JQ85S1MmunQOrKwAAAAAAACrwjcrAAAAAACYCd+smAcrKwAAAAAAwKqwsgIAAAAAgJmwsmIerKwAAAAAAACrwsoKAAAAAABmslDQzAPnSl9WpFSOoYmi/lzk6Whi1qIYn9q4oyjmqzeLVnxcahAZ5yKLXKxpEA/k4tvcPlvi5LZ9ufu1RGvmhaKZlopwdddmrIyilNoiUavvi6CfuWNqidRyx+uS3aJ2cNFYtcdzVq+J+jNjYTRObk3sm2uHYYiiNeuj6GotVa+7NC6aVPIxjG7ojpaC2sjOhnpdf3Gxm9G47trJnUuLMFozu2euj+523DW3cZ7BeDaN5pnbm2d5ELe8Nx0mmRjA6Jrbbd28JLhuXVeeB4xDOYbVHY/k41SdlnHH38f1cyVntFG1Um/6Utt+3TPXzD2C8SFXxgG3zB8685zfbOvbz/Uld5+2CNv3AM9yd23cz3aSnx+76VsfjDsDbxGuFVZWAAAAAAAwgywp52VeAD1oeFkBAAAAAMAcMh/YnAsf2AQAAAAAAKvCygoAAAAAAGbCpzHmwcoKAAAAAACwKqysAAAAAABgBmcf2Dz0UdwfrvhlRSrH0ATpQC6+piVuZ3DbNkQeulgnG/nUEP1ok3qiGC8TETa59Tc+NcteG9cOLvpV8tF5ro1cXGpUb0s0lhP1Jac2TjWK44oif2vr3ZhozWySvNx2ktS7WL3KvnK2rTmmhtjC2n1GRhch2JCU5lLWXDJeNDTbWNmGp7zbNEj6a9hnXfxoXG+5bLcPIkYrYzcjUYSuYyOVG+p1sd/ufoxihl0Mo21f17nlx1gX2RndF26/UTS6YyMPK49Hqu+Hru0vs9+SlmhN9yxviT5v2db1syhWdol9hs/codxHl4pF3mzL88Kof7rIXxevG/VPd6+6NnSx6NG2rv8OZkyKth1lziVo3+2RiXE2m/LrF/cXVlYAAAAAADATVlbMg29WAAAAAACAVWFlBQAAAAAAM+HXUebBygoAAAAAALAqrKwAAAAAAGAOmW9WzIWXFQAAAAAAzCCrLQkM38GvgQAAAAAAgFW50pUVOWeNhYzq3uQRR1LDK5fNtpzhuzvZm30Gx+sjiYumYM1QbxPN60X7LXF52pLPXnZGk10d6YNjcjqT+ezOpQuyrWvz7aN+5trJtcOU/HVx+evumre0vdNH2ezmuqWF1uG5MSuIDrdq75mzbcs7Hs2Y1Pvu2zQ+O+6YWtpwGOracI1LNkvPTEmaTJnk7+P9rvIh1aj+mdByX5S3jY4n2Y5Y3jYau135Zluemg37wdbr9OY5lYPOb59/WzcW+nZwx+TaqAuuW3Q+xX0GxxvO/QqifuauudMHg3fts3xqmIPVtpEkdRtzTMMy/5nazc9y9ucSzYFLNuY8o/26eVYf1Ou41t0Ec9z9rjwuuePdHvt6o7lfrdrr9kqtcU5xHbGyAgAAAAAArArfrAAAAAAAYCasrJgHKysAAAAAAMCqsLICAAAAAIAZ5Cw1fIIMF7CyAgAAAAAArAorKwAAAAAAmEltKhG+25W+rEgpabOtW8zREue3RL1h3FlnooXMdlFkZ21U5ULpP5doh7oo0JboK6el3qX6oDumlqhaV+/Rsb/1XXybiwqOoktd/3WDekvTR1F0jusug4lR67ogC9RoebbVtuG48/UeHZltGxIwXeqeu25RG7lyd90itfeFi0SWfHS0O96pIb5xNNtGUdauHVpip935REP3UPk8SUE0oX2GmXban9ZHjLZwUaDjUL5Zo+ebi3d0853t8Taod6Hnqh0/6vfZmXP1G/ri2ijbiG2Hhravfa5GY6GTl5rIun1G90VlfHEc814XBxxGBZsYchcPfbrf23p9/y2PSS39wYm6yvaofo6Gq8fKCgAAAAAAZsLCinnwsgIAAAAAgJmYBWl4BfjAJgAAAAAAWBVWVgAAAAAAMIOc+TWQubCyAgAAAAAArAorKwAAAAAAmMlCYUcPnNW8rIjidpKJ21FDVJqNNGuISepcDw0ji8pqY+G6YJ8uGstFlkWWiiddKtp0KS7azZ1KNNDVXpsxiG/sN6a/TCYKLUXxd6ZaF6UY9PuNO94DiCIlfSzZvMfyItf2LnZTqo8nDSMwTV9yMWotbOxmcN3cY8iJ4lJ9FKiJ8wzGwdOT+qjKWlEkX+5MnKq5z6MxvzYmuyUWcnLxxSZCVJKSG+9MvW2xm+U2moL2deOH367+eBeLN7djYcO8z/T96L5wY6UbH6IxoDPPRtfPornmxvRvF0cZtW9tf4mjQMtctOZi/XezzIN+sw3GX3NMbmxpaV/Xf6MI0dr2D/sZv59xrazmZQUAAAAAANcd70Tmsa7/HAkAAAAAAB54rKwAAAAAAGAmS/265YOGlRUAAAAAAGBVWFkBAAAAAMAMciYNZC68rAAAAAAAYCZ8YHMe/BoIAAAAAABYlStfWVHK242ird1Smo3JkY7y7V1GtcsGjqTe5JnbLHn//qirXFMUZXH7Nqw/nsmcjsu3z5O/brX569HHbty2rmwaRluvk029YTa76S/j6DKz61/39q5vB6+RXba1uzZRvVGmdolrI8kf78bsM7rfov3WGoZyvZ2JM+/lj3fqzLVpOBe3rRt/U/CavTPbuv4bZa+78tGMkyGbb18+3tNTP+644c71wah9WzLq3XV1981ut8wzIeLG9pZ6h31dh4nmJfaYzPMkmnsMaW/LS8ax/tnYb8yg1WCS70tOvy0fkxt3tsdbf0ym/7p5QEsfdNtGc4/aeiPuWe+OaWOuiySNZt7txg63XaTlug378n1zdFz/o1vnjsnNGc3PCFL98zqak2+2df0w6r/bynpfKXdf4/JYWQEA/1979x9r21nXefzz3b9Ob4tDQbBhWmaosXFSjfywYTBDCCOTsTjE6x/I1DixIoaY+AONRltNxplJSCAzGYaJStIIWg0jkI4MN0YZSXUy88dQKWIUgWpTQNq0FBAYpvaevffZX//YC3t6uevz3Xettc/e5/b9Sprec9ZZaz3rWc96nnXWefb6AAAAANgrvLMCAAAAAIABpHhnxVCYWQEAAAAAAPYKMysAAAAAABhCMrNiKMysAAAAAAAAe4WZFQAAAAAADCLLJDtsZqOHFRHxKUlfkXQkaZmZN0XEMyW9W9LzJH1K0msy84tdC1LF+MxMfJuPYOseoeRU0YQuHmjVo0xzs8xFN7nyrLXHM7lY0zTnRfKxRK5Mmd2jH231FkloLqbKRbvlqooQNOU1yVgx9fXQNdjNxWJJRbygOecuuk2SFh1jAPvEqLn22yfC1aXrVnFVs9l2JrV1jUStoijHJntspe516ON129eLImq1qyrO7NDEZ7oYVnfNVNypqWLfbPSuOdYqHjPNdVOVyY7XZr9VnLXr03wkdRFvbsvULWZRktJEd7u4z9lkZrfryuvGoVUR8+70iXnvqrqnced8ZDLVq/br99m+3aq8q+Ieok2fsdFFy8eqe0Run7jPrvus1+0WIzouJqB3vW+pIjnd7xhuPKmuxa5VWI1hbvxz9w+9zqk51smkuHfuMSbj5F1KL/fPM/MFmXlT8/Vtku7OzBsk3d18DQAAAADAU1auTud/+6bPx0DOSnp58+87Jf0vST/fszwAAAAAAJxK6+hSPgYyhE1nVqSkP4iID0fE65vvXZOZDzf/fkTSNYOXDgAAAAAAPOVsOrPipZn5UER8g6QPRMQnji/MzIyIiz4+ah5uvF6Svu4Zz+1VWAAAAAAA9lb6d5thcxvNrMjMh5r/PyrpvZJeLOmzEfEcSWr+/2jLundk5k2ZedOZpz1rmFIDAAAAAIDLVvmwIiKuioiv++q/Jf1LSR+VdE7Src2P3SrpfdsqJAAAAAAAp0Fmnsr/9s0mHwO5RtJ7m4iYiaT/lpnvj4gPSXpPRLxO0qclvWZ7xQQAAAAAAE8V5cOKzHxA0vMv8v0vSHrFpewsoj3jt8oG7pO/7rjs4IMrpu37LJ48ue2ueuQKd82vdpnNkuQivv26xXYv/ioTSf3ywXO1bN+nOTVVW3FZ3G7dKis6F2a/pq0cmexqSZrNxmbd7teFOx4Xa7Qa+fKOJy6Hvnt2eFfb+jxh1T+4Njp2dd/jibfLQXdtUPLt0B1Lj66uF9dcXBUezn2DSHewW+KOZTL1fejKHI/Lma/6HbvPHm3Ute/lwgxSkhbz9jFhZMYaN85Lvi8cmf7sqCiv2+5Y7f16nzGsfavSqEcfu1yYujflkaSjZXs9jYr2vQ3VWN61nsrt7qCzdPdgfdqDv3/o3j+4tl2ZmGvVSRX3NKYOp7P2X7Hq+9/t3Jwsl+3bdf1vFPf67v6ta3kkaTJpr8ODg/YebTLx5amWDyHl74+wuZMfCQAAAAAAAIxN00AAAAAAAICTu5mNeTliZgUAAAAAANgrzKwAAAAAAGAgexiscSrxsAIAAAAAgIGs+BjIIPgYCAAAAAAA2CsnPrPCRYh1NTXxjaMigs1FIi5NpJZWPeKtXH5YwUUhuRe5VLFvjjtnqyIe08UzVVFejl23R+yei/NzCUvbigmtqsi1Xxv3W8RxufPqlk2mvnF3jQ+r1nOJZv3iPt2xmojAop9z8aR9uMhJVw+roj8bm4gwdyhV5OzBgYl+dMdSXG5Hpn1X6zq23zH9b/WSLRv1Z1Zdukhk+XPu6qFqnksXZdsn9tTUUzVe2H7ULKv67snIxYi2l7e613HH6vrnPvGNTrXdiUl4dRGuZdu3sfSmfosxwa3b56V3Lp57YtrZqoho7BrPXbXfrhHxo4kfy7sOYast/Ym0OqVdd1tdx7b99rj3cOdtWy9tdPGjk6I92Htn0/arezt3nzWbdb+P2lI3+iSZ2asN4AnMrAAAAAAAAHuFd1YAAAAAADCQPjM58QRmVgAAAAAAgL3CzAoAAAAAAAay4p0Vg2BmBQAAAAAA2CvMrAAAAAAAYCCkgQzjxB9WtJ24mYkflaSOqU4b6BbL6eKrKi4CyMalyscZHam9vEc9Iu5cNFYVZ+SiLPtcxC4uamyKlNE9hqprBJjkz42NoeoRc+vi+kYmjk/qHqPm4vgkPyVu1qOtHHVM5q2Os2vUclV97ni6xtH2UdWvix5zkWXbOm/VdtNsd3t16PZZrGuum16xyK4tmf7BnW+p39TWrvU/mfrbla5xflXcsov0HI+7nzfXP2d2i/Nc77e98btI9Sq61NaDWS/D14MbG22kb4/4Rtd/VH3+2N1g9FBFsbauV1xP7lp1sbx1XLjpPxauDdrN2utxPm/frhuHJF/erv3ker8mYrTjOC/5elqZdav6TfMDY7n73yI62t07m32W0aWTbpHUJxFNipPDzAoAAAAAAAaQWf8BD5vhYQUAAAAAAAPhUyDDYKIMAAAAAADYK8ysAAAAAABgIH3erYMnMLMCAAAAAADsFWZWAAAAAAAwgMzslZyFJzCzAgAAAAAA7JUTnVkREZrNLp6hPCoyfB33maDJtMqKbl93uWxft3rKY3O8zaHOisz38+eXxZ4vzmVBS9Ji3r5dlzNdZclvKyfd7tNlZhftrGv+epXNnucXrctcJvnsiqnd7thkVB8tu+XXS93PzapoD6OW679SZZJ3VWWHu/bg1/PLXfW6IkWPx8vLRfu5qfpJx/Xd6ZuDrX/7F4nVdtpDxV0XrolW7ezoqH27K1OH1WVaZdh3tTLlrbgxY2T6paLLsqr+bhumB77vXi7ax1wbd1ec0lHHa8OVR/L3EDHq3s66bjem/jhXy/Zx1V3H1diX5oIcjdtvqat7JWd2ZtapPJKUpt93l0U19rnd9rne3L3UwcF2ruPpQbf7EsmPce6+paoiNya77bqxRJJWpsCuTNUY5so0nXb/VXNktmtvEYrLrUeXdUl4Z8UwmFkBAAAAAAD2Cu+sAAAAAABgIMysGAYzKwAAAAAAwF5hZgUAAAAAAEPI+r1S2AwPKwAAAAAAGECKj4EMhY+BAAAAAACAvbI3MyuqGB8Xx9Mnnm1sdrxatccZVfFAjouEqrbrjnU+b4/qqnSNGD0q4q3csfaJo3TbdVFoVcSoixF1sXp9uLqvokBdxJ2LNbXRePL1a/dZ1K+LozyyEcR2s5a7psqIUVP9Lsqratpdm9Jy6QvsyjS6or27r8rrtuv60Cy3a5apfeVFUQ+unmY9YlpdD+v6yeqPK64PmM228zcFF91WRlLbODl/sL4fbS9UdbMyN/HbdgxTkXFn6sL1d2Us8qp93TQR5tWY4Lg4z4qLEbVxnhMfC+nK5K6LSbFdF8Tq2lIVw1rdQ7Tus4ild23UXTKrorzjsbkHMxuezvwV59ph9MjYdpGdLjLZRWiX+zRtqbreliYK1PWTVVy461v6xOC6tuTaQ3W/3vX+eDLpHuvt7h+qe7s+9wGby3I8xGaYWQEAAAAAAPbK3sysAAAAAADgVMt6FjM2w8wKAAAAAACwV3hYAQAAAADAQDLzVP63iYi4OSLui4j7I+K2iyw/iIh3N8vviYjnHVt2e/P9+yLiu6p98bACAAAAAABYETGW9CuSXinpRknfHxE3XvBjr5P0xcz8JklvkfTmZt0bJd0i6Vsk3SzpV5vtteKdFQAAAAAADCDlU35OuRdLuj8zH5CkiHiXpLOSPnbsZ85K+nfNv++S9MuxjpU5K+ldmXko6ZMRcX+zvf/btrMTfVgR0R4vVEV2ukid5dJFi/lYHBfH4yLjHn/cR4C5NKnlwkTcVZFxph5sbKRPzbLbdR5/7NAuH8/aMyddTGila8RS1XG4eLEqltNxx+riPLelqgcXjeWjQLtfx6MeUbZduWjSio8g9uu6fslFuLqYUMlHax4tuh+sjTbu0Xxd/bs+1EXYSVWMqIvys5vVyvTdLjqvut5c/frotu5xcu4aXxZtxR2Pi0yW/AvHXHlXxTXl+o8jmfZg7h+kuk9rU0VguuUubrJPdKmLEa3iEJeL9jDQPmOjq4cqntRx66YpbxXR2DXmvc8vLS4uNYr2OR633+b3Om+mnrreT1ams/ZzWp03d924ZVVU7cwsX5pY3vreo9s9WFUPLjLVrVtGMZtmODX7rLbruAjzaRGJevk+Qzgx10r6zLGvH5T0T9t+JjOXEfFlSV/ffP+DF6x7rdsZMysAAAAAABhCnuqZFc+KiHuPfX1HZt6xq8LwsAIAAAAAgEHkTmZOD+TzmXmTWf6QpOce+/q65nsX+5kHI2Ii6emSvrDhuk/CCzYBAAAAAEDlQ5JuiIjrI2Km9Qszz13wM+ck3dr8+9WS/jDXn6s8J+mWJi3kekk3SPpjtzNmVgAAAAAAMJBT/DEQq3kHxY9L+p9avxXxHZn5FxHxHyTdm5nnJL1d0m81L9D8G60faKj5ufdo/TLOpaQfy0z7VioeVgAAAAAAgFJm/p6k37vge//22L/PS/q+lnXfKOmNm+6LhxUAAAAAAAwg1T1NCk/GOysAAAAAAMBeOfGZFeOW/OVl8bke97kfl+k8qrKBTdaxyzKunH+8PZPcvR12VexzYjLsDw5MBnWRe72Yt39caG6WTWe+CVWZz13tIuPb1e8Gaw9WjuPs5+FMPbj8b8m3/cXhon3Fg6ndrlvqzlt1Lbrl7pqpnnp37QP6tBV3Tv1Z666qB9cvzU0e/Mzkq1fmc9NPFqfFnbdxx7YiSV27s6odjcziianD5cIMYIWVWXU89vVwZM55ZWSu85U5sW6ZJE2m7decG3MX8/axWirGsEX7FTkqGsto0m28HhXnxnF1WI2b43F7edM1poLbb9dlUl3/bfq8vd/23Ue+jqYH7fdS7poZmfMiSativ12NTV/prpmqHtxYM5m0b3dc3OuvOg6e1djozrn7/WJh+g6p/Xclqegfiu7BjXF97p0nZl13borma9uSOzXV7x4nMuEh63ELm2FmBQAAAAAA2Cu8swIAAAAAgIFcrmkgJ42ZFQAAAAAAYK8wswIAAAAAgEEkaSAD4WEFAAAAAAADyOz38mE8gY+BAAAAAACAvbI3MyuqyBwbZ7SlqEoX8bNc+qdlbt25iSyq4nZcbJmN+Sq266OQ2pe5uLiKOxa3z2pdp3rZjTseV0dVbNaR2e+Zq9pjTZdFvJWbYjY/bI/kqyNlzfVm6qiKfqwiEduU0Y/mcFwdlddbtK/r+oDlstiuvVbb16var2uHfp9F+zX17+Khq/PmyhumqeRyO1Mrq37drmtiRKupoItF+/Kp+ZuCizWtyuQiDav+zP2dw523qkyuf6javqvjybT7rc7C9KNOFYEZ5i9uXaPaJWll2lKfKck+TrVb7KbkoyzdPqtzavsW099VUba2HZrxr4rsdG3fxjcW10XXmPfq0gyytAAADzBJREFUvHVVbdfdQ/gITL/dpdmvvd6qe2c7hnW/3mwzM2Wq7sF8dGn7ei5KteLiVGczX14fZ90t1vQkEV06DGZWAAAAAACAvbI3MysAAAAAADjteMHmMJhZAQAAAAAA9gozKwAAAAAAGEJm+U4ZbIaZFQAAAAAAYK8wswIAAAAAgAGk6rQebOZkH1aEicYpEuNsPJ5pDFVykGtHLqpnOvORnSaVTBOzTxcnJ3WPbqril1zUolu3iovy5e0e8+W4uM8qatW9DMfFMFZxUVMXiWrqt6qHybh9u27dXjGAB7PWZVWsnota7BON5fS5LjLbl7towiqy08VZuWi3qj0cHbkor+7xbI6NlZ70iDvrEc9WDigd7du7slwMqOTbYZ97KHdNVefGnVdnufDLJ5P2vnA8NvWw9PHQ04P226RVj6jbrvGko+peyaxbtRfHjddjM771qSPXVqrhwtXvxNy/ZY84dhdz2yfm3bWHbf0yVEUudo0hr7j46Jm5Fiv2PrbHOOXOzeFhe9/ixk3JH2uflza6Mdn360WEq1k8n5sI7R7Ru5Mev8FOe5xznDxmVgAAAAAAMJBVbucPJ081PKwAAAAAAGAIycdAhsILNgEAAAAAwF5hZgUAAAAAAANIEV06FGZWAAAAAACAvcLMCgAAAAAABtInuQVP2GhmRURcHRF3RcQnIuLjEfEdEfHMiPhARPxV8/9nbLuwAAAAAADg8rfpzIq3Snp/Zr46ImaSrpT0C5Luzsw3RcRtkm6T9PNuIyFp3JJJPJ75zNvlsv3plHtyNTK5wZK0Mtvt48yZ9kztw8P29eZzv12Xg+zyiCuTSftzq6XJoa+ytl2u+3LRvt0qk9yt61SfH1setZfXtaUq891lcbtzeuWVU7tdl0keo/ZzU6Up+fK2b9cdi9R+/UvSyGy3z9Npd11U2/UZ376NduXyzCOK6820h5U559OpP29H5rpw262y5Mdmv64tHRXbdctd5vt0up1PRro6kiRzqdp+x50Xqft1467/ar/VR3SrbXdV1UWb6YG/DXJtaRXt41B1nL5/dv160ceasdONm9OZH2tc/zyZttfhaGY3q/l82bpsZdpvdb5t/ZrtVv26268dN4u/DbryLkwdTWe+/dr7rFH7sU6KvtDV02Le7f5MklamA3Hn7ajYpbts3Lg5nfn20PUeYbHqXkfufr3sH8x4MjaHWtzq237fjX/udztJmpjm7ereHYtU30MMIqVVNfhjI+WdWUQ8XdLLJL1dkjJznplfknRW0p3Nj90p6Xu3VUgAAAAAAPDUscnMiuslfU7Sr0fE8yV9WNIbJF2TmQ83P/OIpGu2U0QAAAAAAE4H0kCGscmc14mkF0l6W2a+UNJjWn/k4+/lem7WRc9IRLw+Iu6NiHsf+8rn+5YXAAAAAABc5jaZWfGgpAcz857m67u0fljx2Yh4TmY+HBHPkfToxVbOzDsk3SFJ137jt/OICQAAAABwWUqlsnpBHDZSPqzIzEci4jMR8c2ZeZ+kV0j6WPPfrZLe1Pz/fVstKQAAAAAA+yz5GMhQNk0D+QlJ72ySQB6Q9FqtP0Lynoh4naRPS3rNdooIAAAAAACeSjZ6WJGZfyrppossesWl7CwiymjDNjMTbdonFifNWzsWJnazikR1kTp9kmxc3I6LPBz1iItzUZXVU0MXNdUnws6tO0oTZ2QinyTpyERYzc+biLUiBsnFX7k4zzr+zsRmmZjLVRH75mLA3DmtHiK7+Lt95OrJxYdVXCxcnziuZXsTLWKP/XYd17dUccpdE2mPiobmovPcNVPGIZrjcX1z13FP8n1sFb/m6mFb0W1V39I1oriKYXXxg+5areK33TV33sR6V2OjSyF2Zeoa0SpJsyva40mrscbFk/apX1dNy0V7h+aiPqU6Trwr19+5Y40iHtr3+93Hmq7lLbdrDsddq9W9s2tLffpY185sn1RdxzYK1PweUMW8m+Xu/sH9HiB1H+urbsc1pa5xqRXXBkfFgcamf6rviZkVwzhdvzkAAAAAAIDL3gk9WwIAAAAA4HKXWvGCzUEwswIAAAAAAOwVZlYAAAAAADCAJA1kMMysAAAAAAAAe4WZFQAAAAAADCT7xD/i753ow4rMbI0euvJMj0kePaJvXASei1g6PG+yHSUdXNFeqKmJHSrSuGy81WzWLQ6x4uKiXFzc+gdM/OuWssWms+0065VpK8uFbw9OHJjy9ogXdBFgJuFyve7URAiaU37gjkW+fbs+vZpKZ6Nh3XV82H0gcdut2rY9HhfLW8adbWeynKvfrhF2kq/Dal3HxTC6vrDqJ11f6Np2FavntuuqoYoftVHXHeNz12Vy/YMvk2sv7nCq2ONcLVqXrUz3PBr5Gwi336np76p6cIsn0x43NcbY3CNUXOxpH+7amD9uosSXc7vdM087aF1mY0KLSGp3HzA12636M3ff4u4v6vuobjG4sx6ZkrPiPsCxsadurOnR77hrvOq7Xf27+l0W5+3goL3+XTzpuMd9tR8bi3XNZdMnGv3I9N0HMxPvWjRfPp1xujCzAgAAAACAIfDOisHwsAIAAAAAgEGkkujSQfCCTQAAAAAAsFeYWQEAAAAAwABS/h032BwzKwAAAAAAwF5hZgUAAAAAAENIokuHwswKAAAAAACwV050ZkVEtOYDu9zg9brty5ZF1rxzYHLHVybgt8rMXszb1x2bTOczV/pTslx2O9aZySOuPPZY+z5XJkda8p/XcvnULrNZkmSyl10udhQZ1F3zzF2etuTzq+datu+zyPh2bcmv57ebabZr8qtnMx9u7erJXVPVeXPH4y7VycTX35HpW+p8+3auTEfmmjlj+itJWszbl9nroghCd/3H4WH7Oa22Wy3vqmqHbaridD3nVfudmXPj+oD53G93ZdadTtvraDr17Wxuxjc39kk+335s6qmqexcR9/j5w9ZlB1ce2O3+g6dPO5XJjSWS7wsn5txU23Xr9rne3DW1Mh3a4tCX15235bLbfZTkj/XMVbP28hT3dofn28drd06r9uvHZHNOi1sAN8a58a0aGyemj3DbraIcu97Oj4r2MHK3NGbdPkOU+6O6638l3x5cP1nd67syud8vDortujId+C7WcvVvlxXXRbc7hEuVRJcOhJkVAAAAAABgr/DOCgAAAAAABpLJOyuGwMwKAAAAAACwV5hZAQAAAADAELJ+Rws2w8MKAAAAAAAGkEqiSwfCwwoAAAAAAAawOjqv//+l+3ZdjMtCVDFNg+4s4nOSPt18+SxJnz+xneNyRlvCUGhLGAptCUOgHWEotCUM5XJuS/84M5/ddyMR8UVJDw9Qnl149hB1MJQTfVjxpB1H3JuZN+1k57is0JYwFNoShkJbwhBoRxgKbQlDoS3hJJEGAgAAAAAA9goPKwAAAAAAwF7Z5cOKO3a4b1xeaEsYCm0JQ6EtYQi0IwyFtoSh0JZwYnb2zgoAAAAAAICL4WMgAAAAAABgr+zkYUVE3BwR90XE/RFx2y7KgNMpIp4bEX8UER+LiL+IiDc0339mRHwgIv6q+f8zdl1W7L+IGEfERyLid5uvr4+Ie5q+6d0RMdt1GbH/IuLqiLgrIj4RER+PiO+gT0IXEfHTzdj20Yj47Yi4gn4Jm4iId0TEoxHx0WPfu2g/FGv/tWlTfxYRL9pdybFPWtrRf2zGtz+LiPdGxNXHlt3etKP7IuK7dlNqXM5O/GFFRIwl/YqkV0q6UdL3R8SNJ10OnFpLST+TmTdKeomkH2vaz22S7s7MGyTd3XwNVN4g6ePHvn6zpLdk5jdJ+qKk1+2kVDht3irp/Zn5TyQ9X+s2RZ+ESxIR10r6SUk3Zea3ShpLukX0S9jMb0i6+YLvtfVDr5R0Q/Pf6yW97YTKiP33G/radvQBSd+amd8m6S8l3S5Jzf33LZK+pVnnV5vf84DB7GJmxYsl3Z+ZD2TmXNK7JJ3dQTlwCmXmw5n5J82/v6L1LwXXat2G7mx+7E5J37ubEuK0iIjrJP0rSb/WfB2SvlPSXc2P0I5QioinS3qZpLdLUmbOM/NLok9CNxNJZyJiIulKSQ+LfgkbyMz/LelvLvh2Wz90VtJv5toHJV0dEc85mZJin12sHWXmH2Tmsvnyg5Kua/59VtK7MvMwMz8p6X6tf88DBrOLhxXXSvrMsa8fbL4HXJKIeJ6kF0q6R9I1mflws+gRSdfsqFg4Pf6LpJ+TtGq+/npJXzo2INM3YRPXS/qcpF9vPlL0axFxleiTcIky8yFJ/0nSX2v9kOLLkj4s+iV019YPcS+Orn5Y0u83/6YdYet4wSZOpYh4mqT/LumnMvP/HV+W64gbYm7QKiJeJenRzPzwrsuCU28i6UWS3paZL5T0mC74yAd9EjbRvE/grNYPwP6hpKv0tdOxgU7oh9BXRPyi1h/Hfueuy4Knjl08rHhI0nOPfX1d8z1gIxEx1fpBxTsz83eab3/2q1MYm/8/uqvy4VT4Z5K+JyI+pfVH0b5T6/cOXN1Mv5bom7CZByU9mJn3NF/fpfXDC/okXKp/IemTmfm5zFxI+h2t+yr6JXTV1g9xL45LEhE/JOlVkn6gefAl0Y5wAnbxsOJDkm5o3m490/rFLOd2UA6cQs17Bd4u6eOZ+Z+PLTon6dbm37dKet9Jlw2nR2benpnXZebztO6D/jAzf0DSH0l6dfNjtCOUMvMRSZ+JiG9uvvUKSR8TfRIu3V9LeklEXNmMdV9tS/RL6KqtHzon6QebVJCXSPrysY+LAE8SETdr/bHZ78nMvz226JykWyLiICKu1/qFrX+8izLi8hVPPBw7wZ1GfLfWnxcfS3pHZr7xxAuBUykiXirp/0j6cz3xroFf0Pq9Fe+R9I8kfVrSazLzwhdNAV8jIl4u6Wcz81UR8Y1az7R4pqSPSPo3mXm4y/Jh/0XEC7R+UetM0gOSXqv1HwPok3BJIuLfS/rXWk+1/oikH9H6M+D0S7Ai4rclvVzSsyR9VtIvSfofukg/1DwM+2WtP2b0t5Jem5n37qLc2C8t7eh2SQeSvtD82Acz80ebn/9Frd9jsdT6o9m/f+E2gT528rACAAAAAACgDS/YBAAAAAAAe4WHFQAAAAAAYK/wsAIAAAAAAOwVHlYAAAAAAIC9wsMKAAAAAACwV3hYAQAAAAAA9goPKwAAAAAAwF7hYQUAAAAAANgrfwdeyKvygXYdigAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# minimize square norm of obs and norm of gradient\n",
    "utils.plot_matrix(small_model.bound_solution.x.reshape(nzyx)[:,5,:],fname='bound.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 1296x1296 with 2 Axes>,\n",
       " <mpl_toolkits.axes_grid1.axes_grid.ImageGrid at 0x7fec0c3272e8>)"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# minimize norm of obs and norm of gradient, no bound constraint\n",
    "utils.plot_matrix(small_model.bound_solution.x.reshape(nzyx)[:,5,:],fname='bound.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.215499 , 6.44882  , 6.693608 , ..., 4.188168 , 4.045181 ,\n",
       "       3.9090075], dtype=float32)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "small_model.obs_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 1296x1296 with 2 Axes>,\n",
       " <mpl_toolkits.axes_grid1.axes_grid.ImageGrid at 0x7f482011a048>)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "utils.plot_matrix(small_model.obs_data.reshape(nzyx[1],nzyx[2]),fname='bound.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: 1754.524425457545\n",
       "     jac: array([-0.16298705, -0.9925626 ,  0.5201423 , ..., -0.08573331,\n",
       "       -0.058479  , -0.04175016], dtype=float32)\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 35\n",
       "    nhev: 4923\n",
       "     nit: 14\n",
       "    njev: 48\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([0.07776316, 0.07238292, 0.06099967, ..., 0.39474226, 0.4014302 ,\n",
       "       0.40053014])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "small_model.bound_solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 1296x1296 with 2 Axes>,\n",
       " <mpl_toolkits.axes_grid1.axes_grid.ImageGrid at 0x7fc7f4777be0>)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "utils.plot_matrix(small_model.solution.reshape(nzyx)[:,5,:],fname='no_bound.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1296x1296 with 2 Axes>,\n",
       " <mpl_toolkits.axes_grid1.axes_grid.ImageGrid at 0x7f28c19a2978>)"
      ]
     },
     "execution_count": 359,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.plot_matrix(small_model.solution.reshape(nzyx)[:,5,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1296x1296 with 2 Axes>,\n",
       " <mpl_toolkits.axes_grid1.axes_grid.ImageGrid at 0x7f28c1a15f60>)"
      ]
     },
     "execution_count": 367,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.plot_matrix(small_model.solution.reshape(nzyx)[:,5,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 364,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1296x1296 with 2 Axes>,\n",
       " <mpl_toolkits.axes_grid1.axes_grid.ImageGrid at 0x7f28c1505978>)"
      ]
     },
     "execution_count": 364,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.plot_matrix(small_model.solution.reshape(nzyx)[:,5,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1296x1296 with 2 Axes>,\n",
       " <mpl_toolkits.axes_grid1.axes_grid.ImageGrid at 0x7febfdf2b8d0>)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.plot_matrix(small_model.obs_data.reshape(small_model.ny,small_model.nx))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1296x1296 with 2 Axes>,\n",
       " <mpl_toolkits.axes_grid1.axes_grid.ImageGrid at 0x7febfddc46a0>)"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.plot_matrix(small_model.kernel_op.gtoep.matvec(small_model.bound_solution.x).reshape(nzyx[1],nzyx[2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1296x1296 with 2 Axes>,\n",
       " <mpl_toolkits.axes_grid1.axes_grid.ImageGrid at 0x7febfdd8ff60>)"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.plot_matrix(small_model.kernel_op.gtoep.matvec(small_model.solution).reshape(nzyx[1],nzyx[2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1296x1296 with 2 Axes>,\n",
       " <mpl_toolkits.axes_grid1.axes_grid.ImageGrid at 0x7fd6a455cef0>)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.plot_matrix(orig_obs.reshape(nzyx[1],nzyx[2]))\n",
    "utils.plot_matrix(small_model.obs_data.reshape(nzyx[1],nzyx[2]))\n",
    "utils.plot_matrix(res)\n",
    "utils.plot_matrix(orig_obs.reshape(nzyx[1],nzyx[2]) - small_model.obs_data.reshape(nzyx[1],nzyx[2]))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
